Question

The manager of a bakery knows that the number of chocolate cakes he can sell on any given day is a random variable having the probability distribution f(x) = 16 for x = 0, 1, 2, 3, 4, and 5. He also knows that there is a profit of $ 1.00 for each cake that he sells and a loss (due to spoilage) of $0.40 for each cake that he does not sell. Assuming that each cake can be sold only on the day it is made, find the baker’s expected profit for a day on which he bakes
(a) One of the cakes;
(b) Two of the cakes;
(c) Three of the cakes;
(d) Four of the cakes;
(e) Five of the cakes. How many should he bake in order to maximize his expected profit?